Irreducible continuous representations of the simple linearly compact n-Lie superalgebra of type S

Abstract

In the present paper, we classify all irreducible continuous representations of the simple linearly compact [Formula: see text]-Lie superalgebra of type [Formula: see text]. The classification is based on a bijective correspondence between the continuous representations of the [Formula: see text]-Lie algebras [Formula: see text] and continuous representations of the Lie algebra of Cartan type [Formula: see text], on which some two-sided ideal acts trivially.